Here's how to tell if a given number is divisible by 13:

Remove the last digit from the number, multiply the value by 9 and then subtract this value from the remaining digits. If what remains is divisible by 13, then the number itself is divisible by 13. You can repeat this procedure multiple times if the result is too big to determine if it is divisible by 13.

For example, 6071. 607 - (1 * 9) = 607 - 9 = 598. It's still to big to determine if this number is divisible by 13, so do it again: 59 - (8 * 9) = 59 - 72 = -13. Since -13 is divisible by 13, 6071 is also.